In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009
Figure 7: pdf of height for varying coherence (other parameters fixed).
4. ACCURACY OF BUILDING HEIGHT ESTIMATION
The accuracy assessment has been carried out with the scheme
described above. Parameter values were chosen in accordance
to the main TanDEM-X specifications. Mutual influence of
following parameters has been investigated:
baseline length
incidence angle
coherence
amount of averaging/smoothing
wavelength
Figure 8 exemplifies the specific case of moderate coherence
(0.6) and only one single look. i.e. the original spatial resolution
is maintained and no smoothing is done. A low coherence has
been chosen by intention, although significantly better values
are expected for TanDEM-X, since clutter may decrease the
coherence in layover areas. The ideal case for this configuration
suggests to selecting a long baseline (e.g. 150m) and a steep
incidence angle (15°), which results in a height accuracy of
approx. 2.5m. Incidence angles less close to the system limits
would yield an accuracy of 5m - 7m.
The effect of improving coherence is illustrated in Figure 9,
where height accuracy is plotted against coherence and various
baselines. It can be seen that, for a baseline of 150m, height
accuracy increases from 2.5m at a coherence of 0.6 up to 1.5m
at a coherence of 0.9.
The final assessment deals with the influence of the number of
looks. A coherence of 0.7 for the case of 200m baseline and 15°
incidence angle enables the derivation of building heights with
lm accuracy for the given viewing geometry (see Figure 10). As
this kind of averaging reduces the spatial resolution, it is
reasonable to investigate the effect of smoothing onto the height
accuracy only up to four looks. What is moreover evident from
Figure 10 is that the increase of height accuracy is significant
from one to two and three looks, but it is then gradually
attenuating - especially for typical coherence values in the
range of 0.6 - 0.8.
As a last remark we refer to the used wavelength (X-band in our
calculations). Equation 7 shows that the RADAR wavelength is
a constant factor for the phase-to-height-sensitivity, which
directly propagates to the standard deviation of height
measurements. A longer wavelength (L-band for instance)
yields a worse phase-to-height sensitivity and consequently a
worse height accuracy. It should be noted, however, that long
wavelengths generally yield better interferometric coherence
depending on the scene characteristics. Hence, this effect could
be partly compensated.
Height Error for Correlation Coefficient = 0.6 and 1 Look
Figure 8: Height accuracy for varying baseline and incidence angle
while other parameters are fixed.
Height Error for 1 Look and Incident Angle = 15®
Figure 9: Height accuracy for varying baseline and coherence while
other parameters are fixed.
Figure 10: Height accuracy for varying looks and coherence while
other parameters are fixed.
5. DISCUSSION AND CONCLUSION
The above analysis shows that space-borne interferometric SAR
systems like TanDEM-X will allow to measure vertical heights
with a standard deviation of roughly 1,5m, which also holds for
the case of moderate coherence in layover areas. Regarding the
application of rapid mapping, this accuracy will certainly allow
the estimation of the number of floors or the detection of
changes in the 3D building geometry. However, baselines and
incidence angles have to be chosen carefully, as they are close
to the technical limits (i.e. “critical baseline” and steep viewing
angle). These constraints can be relaxed when additional data in
form of digital ground plans is available. These allow, for
instance, the utilization of specialized filters instead of simple
multi-looking. The geometry of the filter mask can then be
adapted to the respective building shape to include as much
pixels as possible as observations into the height measurement.
Recall Figure 6 to see how the standard deviation of
interferometric phase improves with increasing number of
observations.
